Comments

Thanks! That's indeed very interesting. I hadn't noticed before that there is such a simple and direct relationship between subject size and the physical aperture diameter ... which probably gives some indication on the limitations of lens designs.

where Ø = f / N is the physical aperture diameter in mm, i.e., B is the ratio of lens diameter and subject size. Sounds almost trivial if expressed this way and reinforces the sensor size independence of the argument. It is part of the equivalence theoreme too (equivalent cameras produce equal images and have equal Ø).

The formula shows that if we use 2x crop sensor, compared to FF sensor, shooting the same Field Of View (same equivalent focal length and same subject framing) and the same aperture, we will eventually lose a total of 4 stops equivalent background blur, which 2 stops come from DOF, plus 2 stops come from Circle of Confusion size (related to magnification or sensor size).

Can we find any sample of real images showing the comparison of background blur of Full Frame vs MicroFourThird, with the same Field of View (same equivalent focal length) and same DOF ? For example sample photos of EM-5 40mm f2.0 vs 6D 80mm f4.0 (same FOV, same subject framing and same DOF).

It will prove whether shooting same subject framing and same subject size, 3 factors which are focal length, aperture and subject size are enough to determine strength of background blur. Or there should be 4 factors which sensor size must be included to determine the strength of background blur.

I guess this is the same issue I mentioned below, i.e. absolute circle of confusion b vs. what you see in the photo which is the relative size of the circle of confusion B = b / w2. The absolute circle of confusion is in fact 4 times smaller for the "same filed of view" scenario. However the sensor is 2 times smaller, so the strength of the background blur is only 4/2 = 2 times smaller in the "same filed of view scenario". Unfortunately I don't have a FF and a MFT to test, but could do so using an APS-C DSLR and a 1/1.7" compact. I know, it sounds counter intuitive, that the sensor size is not included, but indirectly it is by using the real focal length of the lens which is e.g. 2 times smaller for a crop factor of 2. Trust me, it's really only focal length, aperture and subject size ;-)

I have to admit that using small and capital letters b and B may have been a bit confusing. b (= f · ms / N) is the blur disc in absolute terms projected onto the sensor. You need to relate this to the sensor size in order to come to a meaningful metric for the strength of the blur, i.e. relate b to sensor width w2 (please have a look at the first photo above to see what I mean). So B = b / w2 which results in: B = b /w2 = f ·ms / N / w2 = (f ·w2) / (N ·w1) / w2 = f / (N ·w1)You find this towards the end of "Theoretical background" section. This means that the strength of the blur is independent of the magnification, but of course only if you use the real focal length that the lens has and not the equivalent. So for the OMD EM-5 42.5mm f1.8 you really only need to calculate 42.5 / 600 / 1.8 = 3.94%I hope this explains.

Nice article! However, you discard one very important effect, which is the distance between the subject and the background. Your simplified equations are only valid for when this distance is substantially far away.

There is a nice tool to show graphs of the amount of background blur for different sensor sizes and lenses. It can be found at http://howmuchblur.com

You will see that sometimes a certain lens is in the advantage for nearer backgrounds, but loses that advantage for backgrounds which are further away. It is important to also mention this effect.

Indeed you are right. The simplified calculation is only valid, when the background is far away. I personally would consider the estimation to be good enough, once the background distance is let's say 5 times the subject distance (so for a normal portrait maybe larger than 10m), but there is of course no right or wrong. And you also raise a good point, that the behavior of the background blur changes from camera/lens/sensor size combination to combination, as the closer the background gets, the more similar the behavior gets to the DoF definition.Also many thanks for the link. I had not this before. Looks very interesting.

Absolutely brilliant stuff, I never knew how to exactly take the difference in magnification into account when comparing subject separation, but now I know. This makes comparing lenses so much clearer.

I have your blog in a prime place in my bookmarks because it was the only source I had previously found that even touched the interesting subject, but now the formulas are here in full. Thank you!

Your results also show an often overlooked disadvantage of FF sensors like in Sony's RX1: Even at 35mm you have to deal with almost 3% blur. This means that indoors, when taking pics of people, you need to use F4.0 or higher and push up ISO. Compacts like XZ-1/2 can use open apertures an still provide enough DOF.